Locally-Covalent Model of Magnetism of 4f-Metals

Abstract

The electronic structure of rare-earth 4f-metals (REM) is calculated within the many-electron operator spinors (MEOS) representation. Localized 4f-electrons (MEOS Fnr , n=1−7) have spin Sr (MEOS spin factor is crSσ) and orbital moment Lr (MEOS factor is νrL). The 5d-electrons exited on covalent bonds (MEOS is Dr={drσlcrSσνrL}) with amplitude ξD of wave function create the 4f–5d–4f exchange between ions. Localization conditions (drdr=1=FrFr) define MEOS and their secondary quantization by the Bogolyubov Green functions’ method. Spontaneous magnetization, Ms, and ferromagnetic anisotropy (FMA) are expressed through the angular moment Jr (or JT=⟨Jzr⟩). The small value of Tc(TN)≅102 K for heavy REM (except Gd) is defined by unfreezing of sr, lr and ξ2D≪1 of covalent 5d-electrons. Their chemical bond fluctuations (CBF) EDk=Γk2 decrease magnon energy Emk=2AJk2+μ(BA+B) by ΔEm=−ΔAk (ΔA∝T2). FMA field (BA>0) stabilizes FM phase at TT0c, the nonmonotonic Em(k) function changes its sign at k=k0=Qc∝(T−T0c). Destabilized FM phase transforms in helicoid with vector Qc(T)≅0,1 for Tb, Dy, Ho. Application of magnetic field, B=Bc∝(T−T0c)≅1 T, causes the first-kind metamagnetic transition into FM phase. Exchange integral, A(S,L), is composed from spin and orbital parts owing to sr or lr unfreezing. Crystal field (CF) mechanism for FMA is calculated as repulsion of ‘effective charges’ (∝FrDr). H.C.P. deformation (∝uzz≅−10−2) of cubic lattice separates CF anisotropic parts (∝szrSzr and lzrLzr). Their contributions into FMA constants (KCF1,...) depend on the Hund exchange (AD) and on the spin–orbit coupling, λ. Their expression through the Lande’s g-factor (at transition to (JzrJzR)) form) separates critical value g=5/4. When g0 for Tb, Dy, Ho) changes its sign (KCF11) has strong dependence x0(T) in equilibrium (x=x0) owing to CBF. Growth of electrical resistance, R(x), with x growth is explained by change of the Fermi surface near crossing of band spectrum with CBF. The linear part of its dispersion law, ε~(k)∝k, appears. DOS(εF) decreases; the MPD, thermal and other properties change. The model of q-bit is proposed and based on helicoid nanodomains

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